Doctor of Philosophy

Course requirements:
27 units of Math graduate courses numbered between 200 and 297. Students must consult with their Pre-Advisor, Advisor, and/or DGS on appropriate courses. Students who have not completed the Qualifying Exam requirement must enroll in preparation courses in Autumn and Winter of their first year. These courses count toward the 27 units.

Completion of the 1-unit course MATH 355: Graduate Teaching Seminar in the second year of the program.

Additional units should be Math department courses or approved courses from other departments. The course program should display substantial breadth in mathematics outside the student’s field of application.

Qualifying Exams:

Departmental qualifying exams are held in the week before Autumn quarter and in the first week of Spring quarter of the first year of the PhD program to assess student knowledge of core subjects. Students are required to pass qualifying exams in two of four areas:

• Algebra

• Real analysis

• Geometry and topology

• Applied mathematics

Students who do not successfully pass qualifying examinations by Spring quarter of the first year of the PhD program are provided a final attempt the week before Autumn quarter of the second year. Failure to pass qualifying exams on the final attempt results in dismissal from the PhD program. 

Additional details can be found on the Qualifying Exams page opens in a new tab on the department website.

Area Exam:

The student must complete their Area Exam by the end of Winter quarter of the third year.

This exam assesses the student’s breadth of knowledge in their particular area of research. The Area Examination is also an opportunity for the student to present their committee with a summary of research conducted to date and a detailed plan for the remaining research. The Area Exam committee consists of the dissertation advisor plus two additional examiners.

Although teaching is not a requirement for the degree, students may teach as part of the financial support commitment and their professional training.

Admission to candidacy is a prospective judgement by the faculty of a student’s potential to successfully complete the requirements of the degree program. Students are expected to complete qualifying procedures and apply for candidacy by the end of Spring quarter of their second year in the program. Qualifying procedures in the Department of Mathematics include required coursework of 27 units of Math graduate courses numbered between 200 and 297 and MATH 355, identification of a dissertation advisor, and completion of the Qualifying Exam requirement.

In the Department of Mathematics, the oral exam is a defense of the dissertation presented upon the completion of a substantial portion of the dissertation or upon completion of a pre-final draft. A nearly final draft of the dissertation must be submitted to the oral exam committee at least 30 days before the oral exam. Students consult with their dissertation advisor and reading committee members on the timing of the defense. Students are expected to complete this milestone by the end of their fifth year in the program.

Students are required to submit an approved dissertation that makes an original contribution to scientific knowledge in the field of mathematics. Students are expected to submit the dissertation by the end of their fifth year in the program.